Abstract
Current research compares the Bayesian estimates obtained for the parameters of processes of ARCH family with normal and Student's t distributions for the conditional distribution of the return series. A non-informative prior distribution was adopted and a reparameterization of models under analysis was taken into account to map parameters' space into real space. The procedure adopts a normal prior distribution for the transformed parameters. The posterior summaries were obtained by Monte Carlo Markov Chain (MCMC) simulation methods. The methodology was evaluated by a series of Bovespa Index returns and the predictive ordinate criterion was employed to select the best adjustment model to the data. Results show that, as a rule, the proposed Bayesian approach provides satisfactory estimates and that the GARCH process with Student's t distribution adjusted better to the data.
Highlights
A large variety of models exists to estimate the volatility of financial assets return series
Since volatility at a specific time depends on the past values of the series, the determination of maximum likelihood estimators (MLE) of parameters of Autoregressive Conditional Heteroskedasticity (ARCH) family models require the maximization of a non-linear function, and Acta Scientiarum
Whereas Ausín and Galeano (2007) recently suggested a Bayesian approach for Generalized ARCH (GARCH) models with errors generated by Gaussian mixtures, Barreto et al (2008) compared Bayesian and Maximum Likelihood methods by simulated series, following ARCH processes, with different orders and under conditions of finite and infinite variance
Summary
A large variety of models exists to estimate the volatility of financial assets return series. Whereas Ausín and Galeano (2007) recently suggested a Bayesian approach for GARCH models with errors generated by Gaussian mixtures, Barreto et al (2008) compared Bayesian and Maximum Likelihood methods by simulated series, following ARCH processes, with different orders and under conditions of finite and infinite variance.
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